One of the legs of a right triangle measures 2 cm and the other leg measures 1 cm . Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

To find the measure of the hypotenuse in a right triangle, you can use the Pythagorean theorem, which states that \( c^2 = a^2 + b^2 \) where \( c \) is the length of the hypotenuse and \( a \) and \( b \) are the lengths of the other two legs. In this case, \( a = 2 \) cm and \( b = 1 \) cm. Plugging in the values, you get: \( c^2 = 2^2 + 1^2 \) \( c^2 = 4 + 1 \) \( c^2 = 5 \) Now, taking the square root of both sides, we find: \( c = \sqrt{5} \approx 2.2 \) cm (rounded to the nearest tenth). So, the hypotenuse measures approximately 2.2 cm. To make this concept even more fun, imagine you're Sherlock Holmes trying to solve a mystery with mathematical clues! By calculating the lengths of the triangle's sides, you could deduce the perfect spot for a hidden treasure! Every triangle holds secrets just waiting to be uncovered! In real life, understanding triangles isn’t just for detectives—engineers and architects use the Pythagorean theorem all the time to ensure their structures are stable and safe. Whether designing a bridge, a building, or even figuring out the optimal angle for a ramp, this theorem proves essential. So next time you see a right triangle, remember it represents balance and safety in our everyday structures!